## About this Research Topic

The properties of compact stars strongly depend on the equation-of-state of their matter content, which unfortunately is largely unknown. As astronomical objects participate in many different astrophysical processes,

stellar pulsations are a common phenomenon in Astronomy. Non-radial stellar pulsations, in particular, are associated with the emission of gravitational waves, and the frequencies of the modes may give us valuable information regarding the inner structure and composition of the emitting sources. The existence of black holes is by now well established after the historical direct detection of gravitational waves from black hole binaries as well as the first image of the shadow of a supermassive black hole. Perturbed black holes display a characteristic pattern of damped oscillations, and therefore quasi-normal modes, with a non-vanishing imaginary part, are the unique "sound" of black holes.

Regarding black holes, quasi-normal modes only depend on the properties of the geometry (mass, charges, angular momentum, etc) and on the type of perturbation (scalar, vector, tensor, Dirac). Therefore they allow us to test the

Kerr paradigm of General Relativity, and also to test GR in extreme gravitational fields. Of particular interest are the quasi-normal modes for tensor perturbations, which may discriminate between Einstein's theory and alternative theories of gravity. Contrary to GR, where axial and polar modes share equal amounts of radiation, this does not hold in f(R) theories of gravity. Regarding compact objects, Helioseismology investigates the internal structure of the Sun, analyzing the information encoded into the observed spectra. Similarly, gravitational wave Asteroseismology will emerge as a new branch of science, capable of investigating the interior of compact objects, when GW detectors start receiving the gravitational signal emitted by pulsating stars.

We hope that investigators and researchers who work on Solar and Stellar Physics will submit their work to this Research Topic. The principal goal in mind is to deepen our understanding of extreme gravitation and the inner structure of compact stars by studying in detail the expected gravitational signal emitted either from black holes or pulsating compact stars. The areas of interest include but are not limited to:

• Studies of quasi-normal spectra of black holes with different properties as well as in different contexts.

• Studies of non-radial oscillations of relativistic stars assuming different equation-of-states, ideally developing new numerical schemes and putting forward novel ideas.

This Research Topic has been realized in collaboration with Dr. Angel Rincon, Post Doctoral Researcher at Pontificia Universidad Católica de Valparaíso in Chile.

**Keywords**:
Black hole perturbation theory, Composition of astronomical objects, Gravitational wave sources

**Important Note**:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

The properties of compact stars strongly depend on the equation-of-state of their matter content, which unfortunately is largely unknown. As astronomical objects participate in many different astrophysical processes,

stellar pulsations are a common phenomenon in Astronomy. Non-radial stellar pulsations, in particular, are associated with the emission of gravitational waves, and the frequencies of the modes may give us valuable information regarding the inner structure and composition of the emitting sources. The existence of black holes is by now well established after the historical direct detection of gravitational waves from black hole binaries as well as the first image of the shadow of a supermassive black hole. Perturbed black holes display a characteristic pattern of damped oscillations, and therefore quasi-normal modes, with a non-vanishing imaginary part, are the unique "sound" of black holes.

Regarding black holes, quasi-normal modes only depend on the properties of the geometry (mass, charges, angular momentum, etc) and on the type of perturbation (scalar, vector, tensor, Dirac). Therefore they allow us to test the

Kerr paradigm of General Relativity, and also to test GR in extreme gravitational fields. Of particular interest are the quasi-normal modes for tensor perturbations, which may discriminate between Einstein's theory and alternative theories of gravity. Contrary to GR, where axial and polar modes share equal amounts of radiation, this does not hold in f(R) theories of gravity. Regarding compact objects, Helioseismology investigates the internal structure of the Sun, analyzing the information encoded into the observed spectra. Similarly, gravitational wave Asteroseismology will emerge as a new branch of science, capable of investigating the interior of compact objects, when GW detectors start receiving the gravitational signal emitted by pulsating stars.

We hope that investigators and researchers who work on Solar and Stellar Physics will submit their work to this Research Topic. The principal goal in mind is to deepen our understanding of extreme gravitation and the inner structure of compact stars by studying in detail the expected gravitational signal emitted either from black holes or pulsating compact stars. The areas of interest include but are not limited to:

• Studies of quasi-normal spectra of black holes with different properties as well as in different contexts.

• Studies of non-radial oscillations of relativistic stars assuming different equation-of-states, ideally developing new numerical schemes and putting forward novel ideas.

This Research Topic has been realized in collaboration with Dr. Angel Rincon, Post Doctoral Researcher at Pontificia Universidad Católica de Valparaíso in Chile.

**Keywords**:
Black hole perturbation theory, Composition of astronomical objects, Gravitational wave sources

**Important Note**:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.